In order to access hydrocarbon formations from a wellbore, perforating guns have been used to create opening tunnels from the wellbore into the hydrocarbon formation, through which the hydrocarbons can flow out to surface. Deeper tunnels increases the formation exposed to the tunnel and can result in increased productivity from the formation.
Perforating guns generally include a series of shaped charges connected to a detonation system. Each shaped charge generally includes a case, an explosive pellet inside the case, and a metallic cone shaped liner which covers the pellet and enhances penetration depth. The detonation of the explosive pellet generates high pressure gases which propel the liner to collapse at the center line and form a fast moving metallic jet. The tip of the jet can move at speeds of around seven kilometers per second and a tail of the jet in general moves at around one kilometer per second. The symmetry of the shaped charge (case, pellet and liner) affects its ability to form a coherent jet. Asymmetries of the shaped charge result in an incoherent jet which is detrimental to the penetration depth.
In oil filled down-hole applications, the intended target of the shaped charges is the rock formation. Rock formations can have varying strengths and be under varying levels of stress. In instances where the target has a high strength and is under a high stress, the target has a higher resistance to the jet resulting in a reduced penetration depth compared to targets having less strength or under less stress.
According to classical penetration theory, penetration depth (P) is proportional to the jet length (L) and the square root of the ratio of the jet material density (ρjet) and the tail material density ((ρtail) as illustrated by formula I:
  P  =      L    ⁢                            ρ          ⁢                                          ⁢          jet                          ρ          ⁢                                          ⁢          target                    
As such, in order to achieve a deeper penetration, high density materials are utilized in liners. In oil field applications, shaped charge liners are made with powdered metals. The liner density is limited by the density of the commonly used materials, such as tungsten which has a density of 19.3 grams per cubic centimeter.
However, even with denser materials, such as tungsten, packing the powdered metal results in spaces or gaps between the particles which is filled by air, thereby reducing the overall density of the liner. To fill the voids between the tungsten, mixtures of copper (Cu) and lead (Pb) are usually used as a binding material. Both copper (density of 8.9 grams per cubic centimeter) and lead (11.3 grams per cubic centimeter) provide filler and are sufficiently dense so as to not significantly reduce that the overall density of the liner. For example, known commercial shaped charge liners have tungsten content up to 80% by weight, with a density of about 16.0 grams per cubic centimeter.
As shown in formula I, penetration depth is also proportional to the jet length. Generally, jet length is roughly proportional to the ratio of the velocity of the jet tip to the velocity of the tail of the jet. As such, if the jet's tip/tail velocity ratio is high, a deeper penetration depth can be achieved since the jet will stretch longer before it hits the target.
As previously indicated the symmetry of the shaped charge, especially the liner, affects penetration depth. Variations in wall thickness or geometry can have a deleterious effect on the resulting jet, in particular causing the jet to form away from the center line resulting in a jet which varies from a straight, predetermined course toward and into the target formation.
Another factor affect the effective depth of penetration is the slug portion of the jet, which moves slower (−500m/sec.) and is, in general, not capable of penetrating the formation rock. The slug, however, fills the bottom of the perforation tunnel and forms a tight plug. Due to its metallic nature, the slug is not permeable, and thus is it not easily cleaned out from the bottom of the perforation tunnel. As a result, the presence of the slug reduces the tunnel efficiency and thus leads to less productivity from the formation.